Associated spaces defined by ordinary differential equations
type: Item
instance of: scholarly article
title: Associated spaces defined by ordinary differential equations
zbMATH Open document ID: 1107.35005
DOI: 10.4171/ZAA/1295
author: Hoai Le Thu
author: Wolfgang Tutschke
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2006-11-16T00:00:00Z
review text: Summary: The paper deals with initial value problems for desired functions \(u(t,x)\) depending on the time \(t\) and one spacelike variable \(x\). In case the initial function \(\varphi(y)\) satisfies an associated (ordinary) differential equation, the solution \(u(t,x)\) satisfies the associated differential equation for each \(t\). If the general solution of the associated differential equation is known, one gets a system of ordinary differential equations for the desired coefficients depending on \(t\). In any case, the solution can be obtained as fixed-point of a related integro-differential operator.
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35G25
zbMATH DE Number: 5073450
zbMATH Keywords: contraction-mapping principle
zbMATH Keywords: separation of variables
zbMATH Keywords: associated differential equation
zbMATH Keywords: integro-differential operator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/1295
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description: scientific article; zbMATH DE number 5073450